what is the ratio for the surface areas of rectangle prisims shown below given that they are similar and that the ratio of their edge lengths is 7:3

Answer:

$42,890

Step-by-step explanation:

The standard form for an exponential equation is

[tex]y=a(b)^x[/tex]

where a is the initial amount value and b is the growth rate or decay rate and t is the time in years.  Since we are dealing with money amounts AND this is a decay problem, we can rewrite accordingly:

[tex]A(t)=a(1-r)^t[/tex]

where A(t) is the amount after the depreciation occurs, r is the interest rate in decimal form, and t is the time in years.  We know the initial amount (70,000) and the interest rate (.04), but we need to figure out what t is.  If the car was bought in 2006 and we want its value in 2018, a total o 12 years has gone by.  Therefore, our equation becomes:

[tex]A(t)=70,000(1-.04)^{12}[/tex] or, after some simplification:

[tex]A(t)=70,000(.96)^{12}[/tex]

First rais .96 to the 12th power to get

A(t) = 70,000(.6127097573)

and then multiply.

A(t) = $42,890

Answer: The answer is A, because if you subtract 1.3 from 9.2, you would get 7.9, and after that you would divide 7.9 by 4. After doing that, you would get an answer of 1.975, which rounds up to 2.

Step-by-step explanation:

1. Subtract 1.3 from 9.2

2. Take the Answer from Step 1, and divide it by 4

3. Round up your answer.

Answer:

  D:  -5(-6x^2 + x + 2)

  E:  5(2x + 1)(3x − 2)

Step-by-step explanation:

You want to identify the expressions equivalent to 30x² -5x -10.

The first two answer choices have incorrect constants (25 and -2 vs. -10).

A factor of 5 is removed from the remaining answer choices, so let's remove a factor of 5 and see what we get:

  30x^2 -5x -10 = 5(6x^2 -x -2)

An additional x cannot be factored from the expression, so choice C can be eliminated.

Multiplying each of these factors by -1 will make the product correspond to answer choice D.

Factoring will make it correspond to answer choice E, best verified by finding the x-term of the product of the binomial factors:

  E:  2x(-2) +1(3x) = -x, as required

  F:  2x(2) -1(3x) = x, wrong sign

The equivalent expressions are those of choices D and E.

Final answer:

To convert a whole number to a percent, multiply the number by 100. This process turns the whole number into a fraction with a denominator of 100, which can then be written as a percent. This simple multiplication can be done on most calculators.

Explanation:

Converting Whole Numbers to Percent

To convert a whole number to a percent, you simply need to think of the whole number as a fraction with a denominator of 1 and then convert it to an equivalent fraction with a denominator of 100. Once you have this fraction, you simply write it as a percent. Here is a step-by-step process using a calculator:

Since a whole number is over 1, multiply this number by 100. (5 * 100).

The result will be the whole number as a percent (e.g., 500%).

It's important to remember that calculating percents is essentially finding out how many parts out of a hundred the number represents. When using a calculator, this process may involve additional steps or functions, depending on the calculator's design.

For example, with some calculators, you can enter the number, press the multiplication key, enter 100, and then press the equals key to get the percent (e.g., 5 * 100 = 500%).

Remember that calculating percents can be further applied to situations where you have a 'part' and you want to find out what percentage that 'part' is of a 'total'. In such cases, you would divide the 'part' by the 'total' and multiply by 100 to get the percentage. For instance, if 13 out of 35 students in a class wear sandals, the percentage of students wearing sandals can be calculated as (13/35) * 100 which equals approximately 37%.

Answer:

One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph.

Answer:

Step-by-step explanation:

8x+2=-2

Answer:

  A)  The population in the year that she was born.

Step-by-step explanation:

The multiplier of an exponential function is the value that function has when the exponent is zero -- the initial value. The initial value of population in this context is the population in the year Adriana was born.

Answer:

  5 m

Step-by-step explanation:

The perimeter is the sum of the lengths of the four sides. Opposite sides have the same length, so it is twice the sum of the lengths of adjacent sides.

The sum of adjacent sides is (32 m)/2 = 16 m. If one of them is 11 m long, the other is ...

  16 m - 11 m = 5 m

The "missing" side is 5 m long.

let's bear in mind that Y is a bisecting point, so it's really cutting XZ into two equal halves.

[tex]\bf \underset{\textit{\Large 18x-6}}{\boxed{X}\stackrel{12x}{\rule[0.35em]{14em}{0.25pt}} Y\stackrel{12x}{\rule[0.35em]{14em}{0.25pt}}\boxed{Z}} \\\\\\ 12x+12x = 18x-6\implies 24x=18x-6 \\\\\\ 6x=-6\implies x=\cfrac{-6}{6}\implies x=-1[/tex]

If segment XZ is bisected by point Y and XY=12x and XZ=18x-6 then the value of x=-1.

Bisection means division of a line segment into two equal parts by  other line or line segment.

We know that bisector cuts line into equal parts so 2XY=XZ

2(12x)=18x-6

24x=18x-6

6x=-6

x=-1

Hence the value of x is -1 if  XZ is bisected by point Y.

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Answer:

5.75t=p

Step-by-step explanation:

22p=126.50/22

p=5.75 per hour

5.75t=p

The $5.75 is earned for every hour worked.

Answer:

  about 18.8°

Step-by-step explanation:

The depth of the tumor (1.8 cm) is the leg of the right triangle that is opposite the angle of interest. The offset distance (5.3 cm) is the adjacent leg of the triangle.

We know that ...

  tan(angle) = opposite/adjacent = (1.8 cm)/(5.3 cm) = 18/53

Then the angle is found from ...

  angle = arctan(18/53) ≈ 18.76°

_____

The arctangent, or inverse of the tangent function, is also written tan⁻¹. It may be a "second function" of your calculator's tan key.

The angle to aim the gamma ray source to hit the tumor 1.8cm beneath the skin without damaging the vital organ, while moving the source over 5.3cm, can be determined by calculating the inverse tangent (arctan) of the ratio 1.8cm / 5.3cm.

In physics, this problem involves the concept of triangles and trigonometry. Since a right triangle can be formed in this configuration with the distance beneath the patient's skin being one side (1.8cm), the distance over which the radiologist moves the gamma ray source being the second side (5.3cm), the angle required would be an inverse tangent (arctan) of the ratio between these two lengths.

The calculation is thus as follows:

Firstly, set up the ratio of the opposite over the adjacent side of the triangle. This equates to 1.8cm / 5.3cm.

Next, compute the inverse tangent (arctan) of this ratio. You can compute this using a scientific calculator. The answer will be in degrees.

Thus, the required angle to aim the gamma ray source to hit the tumor without damaging the vital organ will be the result of the above calculation.

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Hello There!

The fuel efficiency of a car decreases as tire pressure decreases. The independent variable in the situation is: Tire pressure.

Answer:

A

Step-by-step explanation:

The Price per gallon goes with the fuel efficiency and the speed of the car determines how much gas you use so the answer is A Tire Pressure

Answer:

The answer is :

A. (7x + 4)(7x - 4)

Answer:

The correct answer is first option

(7x + 4)(7x − 4)

Step-by-step explanation:

Points to remember

Identities

(a + b)(a - b) = a² - b²

It is given an expression,

49x² - 16

To factorize  the expression 49x² - 16

We know that 7² = 49 and 4² = 16

Therefore we can write the given expression as,

49x² - 16 = (7x)² - 4²

It is in the form of the above identity,

(7x)² - 4² = (7x + 4)(7x - 4)

The correct answer is first option

Answer:

you would divide 25 by 5.

Step-by-step explanation:

each of the 5 officers would patrol 5 streets with a final of 5 x 5 = 25.

Answer:

5 streets

Step-by-step explanation:

Data:

The number of streets = 25

Number of officers = 5

Each officer will patrol = [tex]\frac{25}{5}[/tex]

                                      = 5 streets

The answer is:

The correct option is:

[tex]D.22\°[/tex]

We can calculate the angle of elevation of the rescue ladder (formed triangle) using the following trigonometric formula:

[tex]Sin(\alpha)=\frac{y}{hypothenuse}[/tex]

Where,

y, is represented by the height where the person is located (50 feet) less the height of the top of the fire truck (10 feet)

hypothenuse, is represented by the length of the ladder (105 feet)

So, substituting and calculating we have:

[tex]Sin(\alpha)=\frac{y}{Hypothenuse}\\\\\alpha =Sin(\frac{Height}{LadderLength})^{-1}\\\\\alpha =Sin(\frac{50feet-10feet}{105feet})^{-1}=Sin(\frac{40feet}{105feet})^{-1}\\\\\alpha=Sin(\frac{40feet}{105feet})^{-1}=Sin(0.38)^{-1}=22.33\°=22\°[/tex]

Hence, we have that the correct option is:

[tex]D.22\°[/tex]

Have a nice day!

Answer:

26

Step-by-step explanation:

If the sides of a triangle are a, b, and c, the triangle inequality theorem tells us, about the sides possible to make up this NON-right triangle:

a + b > c

b + c > a and

a + c > b

Since we have 2 sides, we will call the third unknown side x.  Let a = 12 and b = 14:

12 + 14 > x

14 + x > 12 and

12 + x > 14.

The first inequality, solved for x, is that x < 26.

The second inequality, solved for x, is that x > -2.  We all know that the 2 things in math that will never EVER be negative are distance/length measures and time; therefore, we can safely disregard -2 as a side length of this, or ANY, triangle.

The third inequality, solved for x, is that x > 2.

We now have the solutions for the side length possibilities:

2 < x < 26

From this inequality statement, we see that the longest the side could possibly be and still make a triangle with the other 2 side lengths given, is 26

Answer:

C. 7 inches

Step-by-step explanation:

The Obtuse Triangle Inequality Theorem: c^2 > a^2 + b^2.

14^2 > 12^2 + b^2.

196 > 144 + b^2.

so b < 52. and the square root of 52 is 7.

Thank you and have a great day!

Answer:

Step-by-step explanation:

1^7 = 1

1^9 = 1

1= 1 x 1 or if they really want it 1^2

Answer:

x = -1

Step-by-step explanation:

[tex]\sqrt{1-3x}=x+3\\\\1-3x=x^2+6x+9 \qquad\text{square both sides}\\\\x^2+9x+8=0 \qquad\text{put in standard form}\\\\(x+8)(x+1)=0 \qquad\text{factor}\\\\\left \{ {{x=-8} \atop {x=-1}} \right. \qquad\text{values that make the factors zero}[/tex]

Only the solution x = -1 will work for this equation. The other solution is extraneous.

Answer:

20√2=28.2842....

Step-by-step explanation:

special right traingles

a 45-45-90 states that the legs are congruent and the hypotenuse is leg√2

Answer:

[tex]y=10(2)^x[/tex]

Step-by-step explanation:

This is an exponential function.  Peter is not simply adding $10 a week to his savings, he's doubling each value each week.  The first case of adding $10 a week is linear.  

The standard form of an exponential equation is

[tex]y=a(b)^x[/tex]

where a is the initial amount and b is the growth or decay factor.  We know a = 10 because we are told he started with $10.  After the first week he would have $20 then because $10 doubled is $20.  That coordinate is (1, 20).  We will use that in place of x and y and solve for b:

[tex]20=10(b)^1[/tex]

b to the first is just b, so what we have essentially is 10b = 20, so b = 2.  The equation then is:

[tex]y=10(2)^x[/tex]

Answer:

  5 times as large

Step-by-step explanation:

The ratio of the two numbers tells you how many times as large one is as the other:

[tex]\dfrac{5\cdot 10^5}{1\cdot 10^5}=\dfrac{5}{1}\cdot\dfrac{10^5}{10^5}=5[/tex]

Answer: 5 is the correct answer!

Step-by-step explanation:

Answer:

  A) 255,358.46

  E)  273,353.92

Step-by-step explanation:

The formula for future value of principal P at interest rate r per year compounded n times per year for t years is ...

  FV = P(1 +r/n)^(nt)

Filling in the numbers and doing the arithmetic, we have ...

A) FV = $34,500(1 + 0.069)^30 ≈ $255,358.46

__

E) FV = $34,500(1 + 0.069/365)^(365·30) ≈ $273,352.92

An extraneous solution is a solution that arises during the algebraic process of solving a radical equation but does not actually satisfy the original equation. It is essential to substitute the solution back into the original equation to determine its validity.

An extraneous solution to a radical equation refers to a solution that emerges from the process of solving the equation, but is not a valid solution to the original equation. When we solve radical equations, we often have to square both sides to remove the radical. This process can introduce solutions that aren't true for the original equation. To determine whether a solution is extraneous, we must always substitute it back into the original equation to verify its validity.

If during your process you encounter coefficient terms that correspond to variable-dependent outcomes in function theory, be mindful that the extraneous solutions can impact the interpretation of the solution set. The goal is always to reduce the equation to a state that is readily solvable—via algebraic normal equations in the case of more complex equations like the quintic equation, which sometimes involves elliptic functions for their solution, not to be confused with solutions by radicals.

Equations that are solvable by radicals mean they can be reduced to pure equations using algebraic processes, eliminating the need for other non-algebraic methods. However, during the solution process, extraneous solutions may appear, and thus, it is essential to substitute any found solution into the original equation to ensure it was not introduced during the algebraic manipulations.

Answer:

c. 68, 112

Step-by-step explanation:

The angle is our unknown, so we will call it x.  If the angle is x, then its supplement is 180 - x (supplementary angles add up to equal 180).  The word "is" means "equals", so putting the equation together looks like this:

180 - x = 2x - 24.  Add x to both sides and at the same time add 24 to both sides (combining like terms, in other words):

204 = 3x so

x = 68

x is the angle measure, so the angle is 68 and its supplement is 180 - 68 = 112

The angle will be 68 and its supplement will be 112.

It is given that supplement of an angle is 24 less than twice the measure of the angle.

We have to find out the measure of the angle and its supplement.

What are the supplementary angles ?

The supplementary angles are the angles whose sum is equal to 180° i.e., sum of angles 150° and 30° equal to 180°.

The angle is unknown. Let's assume angle be x.  

We know that , supplementary angles add up to equal 180.

If the angle is x, then its supplement will be :

180 - x ----------- Equation 1

Also ;

angle's supplement is equal to ;

2 × x - 24 ----------- Equation 2

Keeping both the equations equal ;

180 - x = 2x - 24.  

180 + 24 = 3x

204 = 3x

x = 68

Supplement will be ;  180-x = 180 - 68 = 112

Thus , x is the angle measure, so the angle is 68 and its supplement is 112.

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Answer:

4 is the greatest common factor

Step-by-step explanation

The factors of 44 are: 1, 2, 4, 11, 22, 44

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Chance of seed growing into healthy plant:  0.65

Chance of seed NOT growing into a healthy plant:  0.35

To answer this question, we will use the nCr button on the calculator.

In this situation, n = 8   and r = 1.

If 1 seed doesn't grow, then 7 seeds will grow. So will raise 0.65 to the 7th power and 0.35 to a power of 1

7 seeds grow, so we use the 7th power

1 seed doesn't grow, so we use power 1 :

So the answer is:

⁸C₁ × (chance of successful growth)⁷ x (chance of Unsuccessful growth)¹

= ⁸C₁ × 0.65⁷ × 0.35¹

= 0.137   (3sf)

_____________________________

Answer:

Probability that exactly one seed doesn't grow is:

0.137

To calculate the probability in this case, we make use of the Binomial Probability formula. Here, we want to find out the probability that out of the 8 seeds planted, 7 sprout successfully and 1 fails to sprout.

The problem you're working out can be classified under the category of Binomial Probability. A binomial probability problem deals with yes-no scenarios repeated multiple times (like a seed either germinating or failing).

For this problem, we know that the probability of a seed sprouting (success) is 0.65 and therefore the probability of not sprouting (failure) is 0.35 (1 - 0.65). You have 8 seeds, and you want to find the probability that 7 succeed and 1 fails.

The formula for binomial probability is:

P(X=k) = C(n,k) * (p^k) * (q^(n-k))

Where:

By substituting the appropriate values into the formula, we would calculate the binomial probability of exactly 1 seed not sprouting.

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Answer:

[tex]6\ polyphonic\ ringtones[/tex]  and [tex]1\ standard\ ringtone[/tex]

Step-by-step explanation:

Let

x -----> the number of polyphonic ringtones

y ----> the number of standard ringtones

we know that

[tex]x+y=7[/tex]

[tex]x=7-y[/tex] -----> equation A

[tex]3.25x+1.50y=21[/tex] -----> equation B

Solve the system of equations by substitution

Substitute equation A in equation B and solve for y

[tex]3.25(7-y)+1.50y=21[/tex]

[tex]22.75-3.25y+1.50y=21[/tex]

[tex]3.25y-1.50y=22.75-21[/tex]

[tex]1.75y=1.75[/tex]

[tex]y=1\ standard\ ringtones[/tex]

Find the value of x

[tex]x=7-1=6\ polyphonic\ ringtones[/tex]

Answer:

6 polyphonic, 1 standard

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alright. Looking at the graph, angle CGE is equal to angle FGD.

FGD = 90-73

FGD = 17

Therefore, as angle CGE is equal to angle FGD, angle CGE is equal to 17.

Answer: 17 degrees.

By applying angle relationships and recognizing the equality of angles, we determined that angle CGE measures 17 degrees, as it is equal to angle FGD in the context of the graph.

In geometry, analyzing angles within shapes and figures is fundamental. Here, we have a graph depicting intersecting lines and angles. Let's break down the steps and reasoning for finding the measurement of angle CGE:

1. Angle CGE and Angle FGD:

First, we observe the graph and notice that angle CGE is mentioned to be equal to angle FGD. This equivalence allows us to focus on finding the measurement of angle FGD, which, in turn, will be the measurement of angle CGE.

2. Calculation of Angle FGD:

We know that angle FGD is related to a right angle, as indicated by the angle symbol "90" next to it. To calculate the measurement of angle FGD, we use the fact that the sum of angles around a point is 360 degrees, and the angle opposite to a right angle is complementary, totaling 90 degrees.

So, we calculate angle FGD as follows:

Angle FGD = 90 degrees (right angle) - 73 degrees (given angle)

Angle FGD = 17 degrees

3. Angle CGE:

Since angle CGE is stated to be equal to angle FGD, we determine that angle CGE is also 17 degrees.

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A reflection is a transformation where the mirror image of a figure is shown directly opposite its line of reflection.

To find an image that has been reflected across the line y = x, switch the x- and y-coordinates.

Therefore, the rule for reflecting an image across the line y = x can be described as (x, y) → (y, x).

Now, apply rule to coordinates ABC:

A': (2, 3)

B': (1, -4)

C': (-2, -3)

Answer:

got it right on odyssey

A'(2,3)

B'(1,-4)

C'(-2,-3)

Step-by-step explanation:

Answer:

10/3 mph

Step-by-step explanation:

Obviously, (time going) + (time returning) = (total time spent en route) = 54 min.  Since time = distance / rate,

                           3 miles                3 miles

                    ----------------------- + --------------------- = 54 min

                     downhill speed      uphill speed

Let u = uphill speed and d = downhill speed; then d = u + 5 (all in mph)

Then we have:

                           3 miles                3 miles

                    ----------------------- + --------------------- = 54 min

                           u + 5                        u

and our task here is to determine the uphill speed, u.

The LCD is u(u + 5).  Thus we have:

                           3u                     3(u + 5) miles

                    ----------------------- + -----------------------  = 54 min = 0.9 hr

                           u(u + 5)                  u(u + 5)

so that:

             6u + 15

      -----------------------  = 0.9 hr     or      6u + 15 = 0.9(u)(u + 5), or

             u(u + 5)

             6u + 15 = 0.9u² + 4.5u

Combining the u terms, we get:

                      15 = 0.9u² + 4.5u,            or          0.9u² + 1.5u - 15 = 0

Eliminating the fractions, we get                         9u² + 15u - 150, or

                                                                               3u^2 + 5u - 50 = 0

This factors into (3u - 10)(u + 5) = 0.  The only positive root is u = 10/3.

Your average rate on the return trip (uphill) is 10/3 mph (3 1/3 mph).

R is approximately 6 mph.

Let's denote the average rate (speed) on the return trip as
r (in miles per hour, mph). Since it is given that the speed going to campus is 5 mph faster, the speed while going downhill would be r + 5 mph. We need to find the values of r.

The total distance for the round trip is 3 miles to campus and 3 miles back, adding up to 6 miles. The total time for the trip is given as 54 minutes, which we will convert to hours by dividing by 60, giving us 0.9 hours.

The time taken to go to campus is the distance divided by the speed, which is 3 / (r + 5) hours. The time taken for the return trip is 3 / r hours. Since both times add up to 0.9 hours, we can write the equation:

3 / (r + 5) + 3 / r = 0.9

Now we need to solve this equation for r. We find a common denominator and solve:

r(r + 5)(3 / (r + 5) + 3 / r) = r(r + 5)(0.9)

3r + 3(r + 5) = 0.9r(r + 5)

3r + 3r + 15 = 0.9r^2 + 4.5r

6r + 15 = 0.9r^2 + 4.5r

0.9r^2 - 1.5r - 15 = 0

Using the quadratic formula or factoring, we can find the root for r. The root that makes sense in this context (positive speed) gives us the average rate on the return trip.

After solving, we find that r is approximately 6 mph, which is the average speed of the student on their return trip.

Answer:

x-3y-7=0

Step-by-step explanation:

Given

m=1/3

The standard form of point slop form is:

y=mx+b

To find the value of b, we will put the point in the standard form

So,

[tex]-2=\frac{1}{3}(1)+b[/tex]

Solving for b[tex]-2=\frac{1}{3}+b\\-2-\frac{1}{3}=b\\\frac{-6-1}{3}=b\\b=\frac{-7}{3}[/tex]

Putting the values of b and m in standard form:

[tex]y=\frac{1}{3}x+\frac{-7}{3}\\y=\frac{1}{3}x-\frac{7}{3}Multiplying\ both\ sides\ by\ 3\\3y=x-7\\-x+3y+7=0\\Can\ also\ be\ written\ as\\x-3y-7=0[/tex]